Essential Linear Algebra with Applications electronic resource A Problem-Solving Approach / by Titu Andreescu.
Material type: TextPublication details: New York, NY : Springer New York : Imprint: Birkhäuser, 2014Description: X, 491 p. 2 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817646363Subject(s): mathematics | Computer Science | Algebra | Matrix theory | Engineering mathematics | Mathematics | Linear and Multilinear Algebras, Matrix Theory | Algebra | Applications of Mathematics | Game Theory, Economics, Social and Behav. Sciences | Appl.Mathematics/Computational Methods of Engineering | Math Applications in Computer ScienceDDC classification: 512.5 LOC classification: QA184-205Online resources: Click here to access onlinePreface -- Linear Phenomena and Euclidean Spaces of Small Dimension -- Concrete Vector Spaces -- Vector Spaces and Subspaces -- Linear Transformations -- More Matrix Algebra and Determinants -- General Theory of Linear Equations -- Eigenvectors -- Orthogonality -- Forms -- Vector Spaces over Finite Fields -- Appendix A: Complex Numbers -- Appendix B: Polynomials over Complex Numbers -- References -- Index. .
This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject’s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality. Key features include: • a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory; • over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance; • an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them. Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course. .
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